The symmetric driven cavity with sinusoidal forcing for two- and three-dimensions is considered. Results are obtained via numerical computations of the Navier Stokes equations with constant density. The numerical integration is a splitting method, using the Crank-Nicholson method for linear terms and the second-order Adams-Bashforth method for the non-linear terms. Spatial derivatives are evaluated with finite differences, and matrix equations are treated with SOR by lines. The results show symmetric solutions for low Reynolds numbers and asymmetric solutions for higher Reynolds numbers. Subcritical bifurcations are observed for two-dimensional flow. Unsteady flow behavior occurs at higher Reynolds number. Three-dimensional simulations for a cube show only one steady solution.
","abstract_html":"<p>The symmetric driven cavity with sinusoidal forcing for two- and three-dimensions is considered. Results are obtained via numerical computations of the Navier Stokes equations with constant density. The numerical integration is a splitting method, using the Crank-Nicholson method for linear terms and the second-order Adams-Bashforth method for the non-linear terms. Spatial derivatives are evaluated with finite differences, and matrix equations are treated with SOR by lines. The results show symmetric solutions for low Reynolds numbers and asymmetric solutions for higher Reynolds numbers. Subcritical bifurcations are observed for two-dimensional flow. Unsteady flow behavior occurs at higher Reynolds number. Three-dimensional simulations for a cube show only one steady solution.</p>","abstract_has_math":false,"creators":["Osman, Kahar Bin"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["John McHugh"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2004,"date_issued":"2004-01-01T08:00:00Z","date_published":"2004-01-01T08:00:00Z","updated_at":"2026-07-24T05:22:12Z","subjects":["Engineering","Mechanical"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/213","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["John McHugh"]},{"key":"dc:creator","label":"Author","values":["Osman, Kahar Bin"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Engineering","Mechanical"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/213"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["The symmetric driven cavity with sinusoidal forcing for two- and three-dimensions is considered. Results are obtained via numerical computations of the Navier Stokes equations with constant density. The numerical integration is a splitting method, using the Crank-Nicholson method for linear terms and the second-order Adams-Bashforth method for the non-linear terms. Spatial derivatives are evaluated with finite differences, and matrix equations are treated with SOR by lines. The results show symmetric solutions for low Reynolds numbers and asymmetric solutions for higher Reynolds numbers. Subcritical bifurcations are observed for two-dimensional flow. Unsteady flow behavior occurs at higher Reynolds number. Three-dimensional simulations for a cube show only one steady solution.
"]},{"key":"dc:title","label":"Title","values":["Multiple steady solutions and bifurcations in the symmetric driven cavity"]}]}],"canonical_facts":{"dc:contributor":["John McHugh"],"dc:creator":["Osman, Kahar Bin"],"dc:description.abstract":["The symmetric driven cavity with sinusoidal forcing for two- and three-dimensions is considered. Results are obtained via numerical computations of the Navier Stokes equations with constant density. The numerical integration is a splitting method, using the Crank-Nicholson method for linear terms and the second-order Adams-Bashforth method for the non-linear terms. Spatial derivatives are evaluated with finite differences, and matrix equations are treated with SOR by lines. The results show symmetric solutions for low Reynolds numbers and asymmetric solutions for higher Reynolds numbers. Subcritical bifurcations are observed for two-dimensional flow. Unsteady flow behavior occurs at higher Reynolds number. Three-dimensional simulations for a cube show only one steady solution.
"],"dc:identifier":["https://scholars.unh.edu/dissertation/213"],"dc:subject":["Engineering","Mechanical"],"dc:title":["Multiple steady solutions and bifurcations in the symmetric driven cavity"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T05:22:12Z"}